Théoden and Éowyn borne in honour from the Battle of the Pelennor

Men now raised the king, and laying cloaks upon spear-truncheons they made shift to bear him away towards the City; and others lifted Éowyn gently up and bore her after him....

Now slowly and sadly Merry walked beside the bearers.... A great rain came out of the Sea, and it seemed that all things wept for Théoden and Éowyn.... It was through a mist that presently he saw the van of the men of Gondor approaching. Imrahil, Prince of Dol Amroth, rode up and drew rein before them.

Then the prince went from his horse, and knelt by the bier in honour of the king and his great onset; and he wept. And rising he looked then on Éowyn and was amazed. 'Surely, here is a woman?' he said. 'Have even the women of the Rohirrim come to war in our need?'

'Nay! One only,' they answered. 'The Lady Éowyn is she, sister of Éomer; and we knew naught of her riding until this hour, and greatly we rue it.'

Then the prince seeing her beauty, though her face was pale and cold, touched her hand as he bent to look more closely on her. 'Men of Rohan!' he cried. 'Are there no leeches among you? She is hurt to the death maybe, but I deem that she yet lives.' And he held the bright-burnished vambrace that was upon his arm before her cold lips, and behold! a little mist was laid on it hardly to be seen.

'Haste now is needed,' he said, and he sent one riding back swiftly to the City to bring aid. But he bowing low to the fallen, bade them farewell, and mounting rode away into battle.

The Return of the King, LoTR Book 5, Ch 6, The Battle of the Pelennor Fields

Already men were labouring to clear a way through the jetsam of battle; and now out from the Gate came some bearing litters. Gently they laid Éowyn upon soft pillows; but the king's body they covered with a great cloth of gold, and they bore torches about him....

So Théoden and Éowyn came to the City of Gondor, and all who saw them bared their heads and bowed; and they passed through the ash and fume of the burned circle, and went on and up along the streets of stone.

The Return of the King, LoTR Book 5, Ch 8, The Houses of Healing

Then the Prince Imrahil and Éomer of Rohan... mounted to the Citadel; and they came to the Hall of the Tower, seeking the Steward. But they found his chair empty, and before the dais lay Théoden King of the Mark upon a bed of state; and twelve torches stood about it, and twelve guards, knights both of Rohan and Gondor. And the hangings of the bed were of green and white, but upon the king was laid the great cloth of gold up to his breast, and upon that his unsheathed sword, and at his feet his shield. The light of the torches shimmered in his white hair like sun in the spray of a fountain, but his face was fair and young, save that a peace lay on it beyond the reach of youth; and it seemed that he slept.